A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.Comment: 15 pages, 6 figures, email correspondence to [email protected] ; a shorter version of this article appeared in the April 20, 2001 issue of Science; see http://www.sciencemag.org/cgi/content/full/292/5516/47

PasMoQAP: A Parallel Asynchronous Memetic Algorithm for solving the Multi-Objective Quadratic Assignment Problem

Multi-Objective Optimization Problems (MOPs) have attracted growing attention during the last decades. Multi-Objective Evolutionary Algorithms (MOEAs) have been extensively used to address MOPs because are able to approximate a set of non-dominated high-quality solutions. The Multi-Objective Quadratic Assignment Problem (mQAP) is a MOP. The mQAP is a generalization of the classical QAP which has been extensively studied, and used in several real-life applications. The mQAP is defined as having as input several flows between the facilities which generate multiple cost functions that must be optimized simultaneously. In this study, we propose PasMoQAP, a parallel asynchronous memetic algorithm to solve the Multi-Objective Quadratic Assignment Problem. PasMoQAP is based on an island model that structures the population by creating sub-populations. The memetic algorithm on each island individually evolve a reduced population of solutions, and they asynchronously cooperate by sending selected solutions to the neighboring islands. The experimental results show that our approach significatively outperforms all the island-based variants of the multi-objective evolutionary algorithm NSGA-II. We show that PasMoQAP is a suitable alternative to solve the Multi-Objective Quadratic Assignment Problem.Comment: 8 pages, 3 figures, 2 tables. Accepted at Conference on Evolutionary Computation 2017 (CEC 2017